NEW YORK — On “Shameless,” William H. Macy plays the world's most deadbeat dad.

He stars as Frank Gallagher, a boozy, shiftless grifter whose brood of six mix-and-match offspring (do any of them share the same mother?) care for one another and, by necessity, him. The oldest daughter, Fiona (played by Emmy Rossum), is the family's de facto mom, a Wendy to Frank's derelict Peter Pan.

“Derelict” is putting it mildly. Frank is abrasive, self-absorbed, scheming and delusional, a pickled patriarch whose most dignified moments find him passed out on the bathroom floor of the family's ragtag South Chicago digs or on a street corner or maybe in a public park.

But somehow the family stays afloat, even with Frank dragging everybody down.

“For all the craziness they go through, it is a tight-knit family, an honest family that loves each other fiercely,” Macy says. “That's what the show is about.”

Airing Sunday night on Showtime, “Shameless” began its third season recently with Frank coming to in Mexico, not sure how he got there and with no funds or credentials to get himself home.

Ever the schemer, he figures out a way. Just as, this week, he figures out a way to score some drinking money: He volunteers to take a neighbor's infant to the doctor for a scheduled vaccination, then spends the cash meant for the doctor at his favorite bar. He pricks the baby with a thumb tack to simulate a shot and shares a few drops of his whisky to calm the baby's crying.

“I pride myself on taking the script and saying, 'I can DO this!'” says Macy, clearly gleeful at the depths to which Frank routinely sinks. “I take all the stuff the writers can shovel my way!”

Well, almost.

“Once or twice I've said, 'Too much. Too despicable. It's over the line,'” Macy admits with a laugh. “But it's the writers' job to push that line, to put every character in really uncomfortable situations. So we have a good, healthy tug of war.”

The show barrels along a path that is both heartbreaking and hilarious, while Frank sets the pace with his appalling level of substance abuse.

The series doesn't glorify drinking, however riotously drinking is depicted. And “Shameless” recognizes that in a MADD-enlightened era, inebriation is no longer automatically a joke.

“But to claim 'being drunk isn't funny' is not true,” Macy hastens to say. “Being drunk can be very funny!”

It surely has its funny moments, thanks to Frank — and the guy who plays him.

“I flatter myself that, as an actor, I do a pretty good drunk,” says Macy, who, while acknowledging he's on the wagon right now, can draw on “a little firsthand experience.”

He is careful to modulate Frank's drunken state as the day wears on.

“For a scene that takes place at 11 o'clock in the morning, well, that's a four-beer buzz,” he explains, “as opposed to 11:30 at night, when Frank's speech is very slurred.”

Wardrobe helps, too.

“I wear the same clothes almost all the time,” he says. “And I pride myself on this, as does our costumer, Lyn (Paolo): I've never had a fitting. She has sent me pants with the top two buttons missing and the waist too big. So I put a belt on it, I fix it. With Frank, close is good enough.”

If Frank is reliably scruffy, there's one big change coming up. As Macy displays at this recent interview, his hair, previously near shoulder-length, has been shorn.

“I cut it for the show. I cut it on the show in a future episode. I won't give away why,” he says. “And it was a daunting decision. I did have a great head of hair. I'd lived with it for three years, and I'd gotten used to it.”